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Mathematical Problems in Engineering
Volume 2015, Article ID 109325, 9 pages
Research Article

On Two-Level State-Dependent Routing Polling Systems with Mixed Service

1School of Information Science and Technology, Yunnan University, Kunming 650091, China
2Educational and Scientific Institute, Educational Department of Yunnan Province, Kunming 650223, China

Received 19 March 2015; Accepted 1 September 2015

Academic Editor: Ruihua Liu

Copyright © 2015 Guan Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Based on priority differentiation and efficiency of the system, we consider an queues’ single-server two-level polling system which consists of one key queue and normal queues. The novel contribution of the present paper is that we consider that the server just polls active queues with customers waiting in the queue. Furthermore, key queue is served with exhaustive service and normal queues are served with 1-limited service in a parallel scheduling. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we derive the explicit closed-form expressions for the mean waiting time. Numerical examples demonstrate that theoretical and simulation results are identical and the new system is efficient both at key queue and normal queues.